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Given y=ln(1/x)
y'=(1/(1/x))(-x-2)=(1/(1/x))(1/x2)=x/x2=1/x
Use the chain rule. The derivative of ln(x) is 1/x. Instead of just "x" inside the natural log function, it's "1/x". Since the inside of the function is not x, the derivative must be multiplied by the derivative of the inside of the function.
So it's
1/(1/x) [the derivative of the outside function, natural log]
times
-x-2=1/x2 [the derivative of the inside of the function, 1/x]
This all simplifies to 1/x
So the derivative of ln(1/x) is 1/x
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